Season the chicken breasts generously with salt and pepper. Heat 2 tablespoons of butter in a large skillet over medium heat until melted. Cook the chicken breasts for 7-8 minutes per side, or until golden brown and fully cooked through. Remove the chicken from the skillet and set it aside.

Pour the chicken stock or white wine into the same skillet, along with the lemon juice and capers. Increase the heat to bring the mixture to a boil, deglazing the pan by scraping up any browned bits from the bottom to enhance the flavor.

Remove the chicken from the skillet and set aside again. Add the remaining butter and olive oil to the skillet. Stir the mixture over medium heat until the butter melts completely and the sauce begins to thicken slightly.

To serve, arrange the cooked chicken on a platter and generously spoon the creamy caper sauce over the top. This dish is best enjoyed warm.